Simplify; express your answer in exponential form. Assume $y\neq 0, p\neq 0$. $\dfrac{{(y^{-5}p^{2})^{4}}}{{(y^{-3}p^{-2})^{-1}}}$
Explanation: To start, try simplifying the numerator and the denominator independently. In the numerator, we can use the distributive property of exponents. ${(y^{-5}p^{2})^{4} = (y^{-5})^{4}(p^{2})^{4}}$ On the left, we have ${y^{-5}}$ to the exponent ${4}$ . Now ${-5 \times 4 = -20}$ , so ${(y^{-5})^{4} = y^{-20}}$ Apply the ideas above to simplify the equation. $\dfrac{{(y^{-5}p^{2})^{4}}}{{(y^{-3}p^{-2})^{-1}}} = \dfrac{{y^{-20}p^{8}}}{{y^{3}p^{2}}}$ Break up the equation by variable and simplify. $\dfrac{{y^{-20}p^{8}}}{{y^{3}p^{2}}} = \dfrac{{y^{-20}}}{{y^{3}}} \cdot \dfrac{{p^{8}}}{{p^{2}}} = y^{{-20} - {3}} \cdot p^{{8} - {2}} = y^{-23}p^{6}$